Fast Poisson Reconstruction in Python

poisson_reconstruct.py

"""
poisson_reconstruct.py
Fast Poisson Reconstruction in Python

Copyright (c) 2014 Jack Doerner

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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The above copyright notice and this permission notice shall be included in
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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"""

import math
import numpy
import scipy, scipy.fftpack

def poisson_reconstruct(grady, gradx, boundarysrc):
	# Thanks to Dr. Ramesh Raskar for providing the original matlab code from which this is derived
	# Dr. Raskar's version is available here: http://web.media.mit.edu/~raskar/photo/code.pdf

	# Laplacian
	gyy = grady[1:,:-1] - grady[:-1,:-1]
	gxx = gradx[:-1,1:] - gradx[:-1,:-1]
	f = numpy.zeros(boundarysrc.shape)
	f[:-1,1:] += gxx
	f[1:,:-1] += gyy

	# Boundary image
	boundary = boundarysrc.copy()
	boundary[1:-1,1:-1] = 0;

	# Subtract boundary contribution
	f_bp = -4*boundary[1:-1,1:-1] + boundary[1:-1,2:] + boundary[1:-1,0:-2] + boundary[2:,1:-1] + boundary[0:-2,1:-1]
	f = f[1:-1,1:-1] - f_bp

	# Discrete Sine Transform
	tt = scipy.fftpack.dst(f, norm='ortho')
	fsin = scipy.fftpack.dst(tt.T, norm='ortho').T

	# Eigenvalues
	(x,y) = numpy.meshgrid(range(1,f.shape[1]+1), range(1,f.shape[0]+1), copy=True)
	denom = (2*numpy.cos(math.pi*x/(f.shape[1]+2))-2) + (2*numpy.cos(math.pi*y/(f.shape[0]+2)) - 2)

	f = fsin/denom

	# Inverse Discrete Sine Transform
	tt = scipy.fftpack.idst(f, norm='ortho')
	img_tt = scipy.fftpack.idst(tt.T, norm='ortho').T

	# New center + old boundary
	result = boundary
	result[1:-1,1:-1] = img_tt

	return result